On Construction of Two-stage Response Surface Designs

Consider the common situation in many response surface applications. In the first stage, a two-level design and central point(s) have been conducted, and the analysis indicated that the curvature of the response surface is significant. In such a scenario, a second stage of experiments is called for so that a second order model can be fitted. The problem of constructing two-stage response surface designs with high efficiency is studied in this paper. The focus will be on the design of experiment for the second stage. The appropriateness of the well-known D-optimal criterion for designing the second stage experiments is first discussed. A new criterion, C-optimality, is then proposed to find design points in the second stage, given the points in the first stage. The proposed criterion is a weighted sum of efficiency measures from four subsets of parameters in a second order model. By selecting suitable weights, one can construct two-stage response surface designs with evenly high estimation efficiencies for all the parameters. A construction algorithm is then introduced. The superiorities of new designs are demonstrated by a thorough comparison with existing designs.